The number of sub-categories within these major types varies.
The Beer Judge Certification Program (BJCP) 2008 Styles has 23 main categories and 81 sub-categories or styles (see Classic Styles Spread Sheet).
They also list 5 categories of Ciders and Meads (an alcoholic beverage, made from fermented honey and water).
BeerAdvocate.com has over 100 styles (popular ones are listed above and in the body of this page), and Beer 101 - Styles at ExploreStLouis.com has 8 as follows:
Lager: Pilsner (Includes most domestic types) and Bocks
Ale: IPA, Brown, Amber, American Pale, Wheat, American Stout

The term lager comes from the German word, "lagern," which means to store away (cellar). Lagers are brewed using bottom fermenting yeasts at cool temperatures near 50-55°F (cooler than ales). The lager yeasts produce less byproducts than ale yeasts and normally result in a more simple and crisp flavor. characteristically smooth, elegant, crisp and clean. The lower temperatures require longer fermentation periods and these beers are then stored away for weeks (at about 35°F) before maturing.

Some systems have only two sub categories of Lager, Pilsner
Brands below are just a few examples of some of the popular beers in each category.
Scores (A-F) from BeerAdvocate.com

Lower in calories and carbohydrates compared to other beers. Typically a high amount of cereal adjuncts like rice or corn are used to help lighten the beer as much as possible. Very low in malt flavor with a light and dry body. The hop character is low and should only balance with no signs of flavor or aroma. European versions are about half the alcohol (2.5-3.5% abv) as their regular beer yet show more flavor (some use 100% malt) then the American counterparts.Sam Adams Light B- (Boston), Yuengling Light Lager C (Penn.), Tsingtao Draft Beer C (China), Molson Canadian Light C- (Canada), Amstel Light D+ (Netherlands), Michelob Ultra Amber D+, Coors Light D-, Michelob Ultra F, Corona Light FJuly 2007 Consumer reports top 10 in order (Very good): Michelob Ultra Amber, Michelob Light, Michelob Ultra, Coors Light, Sam Adams Light, Budweiser Select, Busch Light, Bud Light, Natural Light, Miller Lite

A style of lager made famous in Pilsen, Czechoslovakia that is hoppier than your standard lager.
They are brewed mostly with pils malts and European / German noble hop varieties.
The aromas and flavors display grainy and sometimes biscuit-like malts (honey and sulfur-like accents are not abnormal), yet normally feature most prominently a firm hop presence which can yield a strong bitterness and floral, spicey, or grassy qualities. Gordon Biersch Pilsner B-, Becks C (German)American Double / Imperial Pilsner:
Similar to a Pilsner in appearance, but expect a more pronounced malty backbone and an intense bitterness.
Samuel Adams Hallertau Imperial Pilsner A-

Vienna lager is brewed using a three step decoction boiling process.
They are an amber to copper or even reddish brown color. They are medium-bodied malty (toasted or light roasted features) beers with only a mild sweetness, a lightly bitterred hop balance, and a somewhat dry finish.Samuel Adams Boston Lager® B+ (Some experts consider it too hoppy to be a Vienna) , Dos Equis Amber Lager C+ Mexico

The beer's grist bill is cut by using large portions of rice, but not enough to be classified as Happoshu. Pale yellow in color, soft hop nose, and expect a rounded, firm malty character, moderate bitterness, and a trademark dry finish.Sapporo and Asahi are produced in Canada, under the supervision of the parent companies, while Kirin is produced at an Anheuser-Busch facility in Los Angeles.Sapporo Premium Beer C, Kirin Ichiban C-, Asahi Super Dry C-

A deep golden (Helles Bocks & Maibocks) to brown (Traditional Bocks) colored lager, which originated in the German town of Einbeck as early as the 14th century. After being resurrected in Munich three centuries later, this style errantly became known as "bock" (which also means "billy-goat" in German) instead of "beck." The bock beer is malty rich and sweet (but not overly sweet) and typically contains bready, toasted, even caramel flavors that are in some cases lightly balanced but never overcome by hops. The alcohol level is higher than the average beer but does not dominate the aroma or flavor. The body of a bock is medium to just under full-bodied. The smooth character of a lager should come through in the bock.Samuel Adams Winter Lager B, Samuel Adams Chocolate Bock B+

Straw to pale amber in color, most use excessive amounts of adjuncts, such as corn, rice, refined brewers sugar (dextrose) and as a result there are very few "all malt" brewed malt liquors. Hops are barely used.
Higher alcohol versions tend to have a loads of fusel alcohol, which gives off solvent or fuel like aromas and flavors.
Some breweries enable the use of special enzymes to further breakdown the malt and adjuncts so they will yield a larger percentage of alcohol. This makes for quite a dry beer, with only a small amount of unfermented sugars and a kick
Colt 45 Malt Liquor D+, Molson XXX C-

Ales are brewed using top fermenting yeasts at temperatures normally in the 60-75°F range. These yeasts normally produce additional fruity type flavors and the higher temperatures result in fast (one week) fermentations.

A "catch-all" category of ales that has a broad spectrum of attributes, amber or red ales encompass those hard to classify beers with more color than an American pale ale but less than a brown ale (the amber to copper range). Because of their diversity, amber ales can have low to high malty character (although most are moderate to high with caramel representing the most common component of both aroma and flavor) and a hop level (citrus aromas and flavors common) that is anywhere from supporting and balanced to aggressive. The mouthfeel of an amber ale is heavier than an American pale ale (APA) and the roasted character nearly absent relative to an Irish red ale.Fat Tire Amber Ale B (CO), Red Tail Ale B- (Mendocino Brewing), Leinenkugel's Classic Amber C+ (Jacob Leinenkugel, Wisc.)

Pale Ales are brewed with pale malts and are generally lighter in style than
regular (bitter) ales.
There are several types English, India and American.
The English Pale Ale can be traced back to the city of Burton-upon-Trent, a city with an abundance of rich hard water. This hard water helps with the clarity as well as enhancing the hop bitterness. This ale can be from golden to reddish amber in color with generally a good head retention. A mix of fruity, hoppy, earthy, buttery and malty aromas and flavors can be found. Bass Pale Ale B- (England), Sierra Nevada India Pale Ale B, Long Hammer IPA C+ (Redhook brewery), Boddingtons Pub Ale B- (England)

India Pale Ales First brewed in England and exported for the British troops in India during the late 1700s. To withstand the voyage, IPA's were basically tweaked Pale Ales that were, in comparison, much more malty, boasted a higher alcohol content and were well-hopped, as hops are a natural preservative.Long Trail Traditional IPA B (Vermont), Harpoon I.P.A B (Boston), Sierra Nevada Celebration Ale A-

American Pale Ales (APA) tend to be cleaner and hoppier, while British tend to be more malty, buttery, aromatic and balanced.
Generally, expect a good balance of malt and hops. Fruity esters and diacetyl can vary from none to moderate, and bitterness can range from lightly floral to pungent.Sierra Nevada Pale Ale A- (Chico, Calif.), Mirror Pond B+ (Deschutes, Oregon), McSorley's Ale C+ (Pabst, Ill.)

Irish Red Ales originated in Ireland and are known for their drinkability. They are generally clean and malty with an initial sweetness and a roasted dryness in the finish. Some examples may have a light buttery character and a low hop profile. Typically this ale is amber to deep reddish copper in color and clear. Most examples are 4% to 6% ABV.Smithwick's Ale B (Ireland) Smithwick's Brewery, Smithwick's B (Ireland) Guinness,
Samuel Adams Irish Red B+ (Boston)

Scottish Ales originated in Scotland and are generally clean and malty with perhaps a faint touch of smoke and few fruity esters. Most examples have a low hop profile due to the historical fact that hops are not grown in Scotland and expensive imported hops were, therefore, used sparingly. Some examples also have a peaty character which is typically perceived as earthy, smoky or very lightly roasted. Typically this ale is clear, deep amber or dark copper in appearance, although the stronger versions can be dark brown in color. Alcoholic strength can range from a low of 2.5% to around 10% ABV.Wee Heavy A-, St. Andrew's Ale B+ and Belhaven Scottish Ale B+ (Belhaven Brewery Scotland), Arran Dark B (Isle of Arran, Scotland) Long Trail Hibernator B (Vermont), Kilt lifter B- (Arizona), Celtic Amber B- (Sacrameto)

A reddish-brown ale made with dark or brown malt.
Before 1700, nearly all beers were considered brown ales, but "brown ale" as a specific beer style is a relatively modern invention. Today's versions are slightly sweet, have a nutty flavor and restrained bitterness, with an obvious malt character, balance, and smoothness.
Typically rich without being
filling, displaying hints of chocolate and fruity sweetness with varying degrees
of bitterness. Known in England as a "thirst-quencher".NEWCASTLE Brown ale B-; smooth, nutty flavour, slight hoppiness (United Kingdom), Pete's Wicked Ale B- (Texas)

The darkest of beers, are made with highly roasted malts, barley, and differentiated by their brown-black colour, chocolate-coffee flavours, and fuller body.GUINNESS Draught B (Dublin, Ireland)
American Stouts:Black Hawk Stout B (Mendocino Brewing)

Oatmeal Stouts are generally medium to full bodied stouts that have an unreal smoothness to them from the addition of oats to the mash. The oats not only add a lot of smoothness to the mouth feel but give a touch of sweetness that is unlike any other type of stout.Samuel Smith's Oatmeal Stout A- (England)

Generally light in hops and heavy in carbonation, wheat ales are made from
wheat, instead of barley, by top fermentation. Wheat ales are unfiltered, usu-
ally very pale and cloudy in appearance, and effervescent on the nose.
Dark: Lunar B- (Boulevard Brewing, Missouri)
Pale: Samuel Adams Summer Ale B-

A Belgian Style ale that's very pale and cloudy in appearance due to it being unfiltered and the high level of wheat, and sometimes oats, that's used in the mash. Always spiced, generally with coriander, orange peel and other oddball spices or herbs in the back ground.
Sometimes served with a lemon, but if you truly want to enjoy the untainted subtleties of this style you'll ask for yours without one.Blue Moon Belgian White (Coors) B-, Allagash White (Maine) A-, Sam Adams White Ale B

Most examples of this style will be copper in color with a mild caramel-malt aroma. Some examples will also have hop and fruit notes in the aroma. The flavor will typically be bitter with caramel, noticeable fruity esters and earthy or floral hops. A very drinkable ale.Honker's Ale B (Goose Island, Ill)
Extra Strong Bitter (ESB):Redhook ESB B- (WA)

Fruit Beer

A style that is broad and diverse and which captures beers with fruit added in the recipe or base style. The fruit flavors can be obtained via addition of real fruits, extracts, or syrups and artificial flavorings at multiple points in the brewing process. The fruit beer classification does not include beers with natural fruity flavors derived from yeasts, malts, or hops.

Black and Tan
US:
1/2 glass Bass Pale Ale
topped off with Guinness Draught (not Extra Stout)
Guinness is less dense so floats on the top.
Half & Half
Larger & Stout
Harp Lager & Guinness.draught How to mix youtubeBlack & Tan
Guinness promotional advertising refers to a Black & Tan
as being the Bass pale ale and Guinness stout.
Sometimes Black & Tan and Half & Half are used interchangeably.
According to "The Guinness Drinking Companion" by Leslie Dunkling:
* Black and Tan = Guinness and Mild
Mild - Dark brown (occasionally pale) English and Welsh beer, lightly hopped.
* Half and Half = Mild and Bitter
Bitter - British term for the pale, amber or copper-colored beers
that developed from the pale ales in the 19th century.
In Dublin, where Mild is no longer available, you will get
Guinness mixed with Bitter if you ask for a Black and Tan.
[Note: Mild is a sweet 'Tan' coloured beer.,
that is typically light in alcohol.]
Republic of Ireland:
Half pint of Smithwick's topped off with Guinness
Boilermaker
2 oz whiskey
10 oz beer
Beer mixed-drink recipes at DrinksMixer.com

Fox And Hound Smokehouse & TavernReview at BeerAdvocate says they are overpriced.

Other:"Green" Beer at the Sierra Club
Health:
Beer has generally been considered bad for you and not a good thirst quencher because of its diuretic effect. However,
in a 2007 Study at Granada University by Professor Manuel Garzon,
25 students were asked to run on a treadmill under stifling temperatures of 40° C (104° F) until they were close to exhaustion.
Their hydration levels, concentrationability and motor skills were later measured by the researchers.
While half were given two half pints of Spanish lager to drink, the rest were provided water. Both groups were then allowed to drink as much water as they wanted.

Professor Garzon said the rehydration effect in the students who were given beer was slightly better than those given water.

In a 2012 article in California Adventure Sports, Derrick Peterman, beer-runner.blogspot.com, did his own research on the web and by emailing Prof. Garzon.
Turns out Garzon's study was never published, and he doesn't think beer has any advantage.
Peterman's conclusion was beer probably doesn't help physiologically, but isn't too bad and can be a motivational factor.
.
See more at alcohol under health.